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Apr 3, 2024

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Name e, 174 Planetary Orbit Simulator — Student Guide V\yan (/7(0;\/1 Background Material Answer the following questions afier reviewing the “Kepler's Laws and Planctary Motion” and “Newton and Planetary Motion” background pages. Question 1: Draw a line connecting each law on the left with a description of it on the right. Kepler’s 2™ Law only a force acting on an object can change its motio planets move faster when close to the sun planets orbit the sun in elliptical paths planets with large orbits take a ong time to complete an orbi Question 2: When written as P> = a’ Kepler's 3rd Law (with P in years and a in AU) is applicable to ... a) any object orbiting our sun. b) any object orbiting any star. ) any object orbiting any other object. Question 3: The ellipse to the right has an eccentricity of about ... a) 0.25 b) 0.5 © 075 d) 0.9 Question 4: For a planet in an elliptical orbit to “sweep out equal areas in equal amounts of time” it must . a) move slowest when near the sun (® move fastest when near the sun c) move at the same speed at all times d) have a perfectly circular orbit NAAP — Planetary Orbit Simulator 1/8
Oueation 5 1170 planet i iwice a8 fatr (Yoo the oo of aphe m than at perih . then 1h wtrenpth of the gravitational force sl aphelion will be a) four times as much b)) twice as much ¢) the same d) one half as much @ one quarter as much Kepler's 1st Law If you have not already done so, launch the NAAP Planetary Orbit Simulator « Open the Kepler’s 1% Law tab if it is not already (it's [ rjp: You can change open by default). the value of a slider f A by clicking on the « Enable all 5 check boxes. slider bar or by entering a number n e The white dot is the “simulated planet”. One can click on the value box. it and drag it around. « Change the size of the orbit with the semimajor axis slider. Note how the background grid indicates change in scale while the displayed orbit size remains the same. « Change the eccentricity and note how it affects the shape of the orbit. Be aware that the ranges of several parameters are limited by practical issues that occur when creating a simulator rather than any true physical limitations. We have limited the semi-major axis to 50 AU since that covers most of the objects in which we are interested in our solar system and have limited eccentricity to 0.7 since the ellipses would be hard to fit on the screen for larger values. Note that the semi-major axis is aligned horizontally for all elliptical orbits created in this simulator, where they are randomly aligned in our solar system. « Animate the simulated planet. You may need to increase the animation rate for very large orbits or decrease it for small ones. « The planetary presets set the simulated planet’s parameters to those like our solar system’s planets. Explore these options. Question 6: For what eccentricity is the secondary focus (which is usually empty) located at the sun? What is the shape of this orbit? OQC, Tltl\s mq)(p 9 Fg,( {'ZLT (}rc/e Question 7: Create an orbit with a =20 AU and e = 0. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r; and r; at these locations? NAAP — Planetary Orbit Simulator 2/8
\ [ mmn’ r2 (AU) %"%"W,,2O | 2O Far Right 20 i ;_2 Og, — Question 8: Create an orbit with a = 20 AU and ¢ = 0.5. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r; and rp at these locations? r (AU) r2(AU) RTINS 00§11 NS ) Vlrfur Right 30 ‘ 0 Question 9; For the ellipse with a =20 AU and e = 0.5, can you find a point in the orbit where 1, and r; are equal? Sketch the ellipse, the location of this point, and r; and ry in the space below. value of the sum of r; and r, and how does it relate to the ellipse - i - . A Iues:! 1S thas true for pses”? . [ OF all CLIPSC 13 Ty, U € AaV1 )< L YK
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